WORD PROBLEMS ON MULTIPLYING AND DIVIDING FRACTIONS

Solve the following fraction word problems. Cancel and simplify your answers.

Problem 1 :

A stack of boards is 21 inches high. Each board is 1 3/4 inches thick. How many boards are there ?

Solution :

A stack of boards is 21 inches high.

Thickness of each board = 1  3/4 ==>  7/4

Number of boards = 21 ÷ 7/4

= 21 ⋅ (4/7)

= 12

So, the number of boards is 12.

Problem 2 :

A satellite makes 4 revolutions of the earth in one day. How many revolutions would it make in 6 1/2 days.

Solution :

A satellite makes 4 revolutions of the earth in one day.

Required to find number of revolutions it will make in 6  1/2 days.

= 4 ⋅ 13/2

= 26

So, the number of revolutions is 26.

Problem 3 :

A bold has 16 1/2 turns per inch. How many turns would be in 2 1/2 inches of threads ?

Solution :

A bold has 16 1/2 turns per inch.

Required to find number of turns in 2 1/2 inches of threads.

Converting 16  1/2 and 2  1/2 to improper fraction, we get 33/2 and 5/2 inches respectively.

= 33/2 × 5/2

= 165/4

= 41 1/4

Problem 4 :

If a bookshelf is 28 1/8 inches long, how many 1 7/8 inch thick books will it hold ?

Solution :

Length of bookshelf = 28 1/8

= 225/8

Thickness of a book = 1 7/8

= 15/8

So, total book will hold = (225/8) ÷ (15/8)

= (225/8) ⋅ (8/15)

= 225 ÷ 15

= 15

It will hold 15 books.

Problem 5 :

Deborah needs to make 16 costumes for the school play. Each costume requires 2 1/4 yards of material. How many yards of material will she need ?

Solution :

Deborah needs to make 16 costumes for the school play.

Each costume requires 2 1/4 yards of material.

= 16 × 9/4

= 36

So, she will need 36 yards of material.

Problem 6 :

The Coffee Pub has cans of coffee that weigh 3 1/4 pounds each. The Pub has 8 1/2 cans of coffee left. What is the total weight of 8 1/2 cans ?

Solution :

The Coffee Pub has cans of coffee that weigh 3 1/4 pounds each.

The Pub has 8 1/2 cans of coffee left.

= 3 1/4 × 8 1/2

= 13/4 × 17/2

= 221/8

= 27 5/8

So, the total weight of 8 1/2 cans is 27 5/8.

Problem 7 :

Belinda baked 9 pies that weigh 20 1/4 pounds total. How much does each pie weigh ?

Solution :

Number of pies = 9

Weigh of pounds = 20 1/4

= 81/4

Weight of each pie = (81/4) ÷ 9

= (81/4) × (1/9)

= 9/4

= 2   1/4

So, weight of each pie is 2   1/4.

Problem 8 :

A piece of paper is 4/1000 inches thick. How many sheets of paper will it take to make a stack 1 inch high ?

Solution :

A piece of paper is 4/1000 inches thick.

Number of sheets will be required = 1 ÷ (4/1000)

Multiplying 1000 on each sides.

= 1000 ÷ 4

= 250

So, 250 sheets of paper will be required to make a stack 1 inch high.

Problem 9 :

Tanya has read 3/4 of a book, which is 390 pages. How many pages are in the entire book ?

Solution :

Let x be the total number of pages in the book

3/4 of x = 390

x = 390 (4/3)

x =  520

So, the pages are in the entire book is 520.

Problem 10 :

DJ Gabe is going to serve 1/3 of a whole pizza to each guest at his party. If he expects 24 guests, how many pizza’s will he need ?

Solution :

Quantity of pizza he will serve = 1/3

He expects the guests is 24.

= 1/3 of 24

= (1/3) x 24

= 8

So, 8 pizza’s he will need.